Instructions: Please Read!

  • The final examination contains seven questions.
  • Answer all questions on the examination pages (you will undoubtedly need to create space to do so.)
  • Show all of your work to receive partial credit.
  • Write and/or word process neatly and legibly.
  • The final examination is due office by 12:00PM Friday May 8.
  1. (25 points) Below are actual data on three open –end, S&P 500 index funds. The objective of all three funds is to mimic the return on the S&P 500 stock market index. All three funds are priced at 1/10 (10%) of the actual value of the S&P 500. For simplicity, assume the S&P 500 index is currently at 1500.

The three funds are offered by Vanguard Securities (symbol vinix); Morgan Stanley (symbol spiax); and UBS (symbol pwsbx), respectively.

Data and information on the funds is presented below

FundFront-end load Back-end load Management Fee Expense Ratio 12b-1 Fee

VINIX 0.00% 0.00% 0.05% 0.05% 0.00%

SPIAX 5.25% 0.00% 0.12% 0.59% 0.25%

PWSBX 0.00% 3.00% 0.20% 1.10% 0.65%

Suppose you plan to invest $1,000 in one of these funds for one year.

A.What price per share/Net Asset Value will you pay for each of the three funds? How many shares of each fund will you receive for your $1,000 initial investment?

B.Suppose the S&P 500 increases in value by 10 percent during the next twelve months, and you then sell your shares. What will be the respective rates of return on the three funds? Which fund offers the highest return?

C.The S&P 500 "SPDR" (symbol SPY) is an Exchange Traded Index Fund also designed to replicate the return on the S&P 500. It is also priced at 10 percent of the S&Ps 500 value.

Suppose you decide to invest your $1,000 in the S&P 500 via the SPY Exchange Traded Fund rather than the open-end funds above. Also suppose there is a $15 brokerage fee when you purchase and again when you sell SPY shares via either an on-line or ‘full service’ brokerage firm. What will be your rate of return, again assuming the S&P 500 rises 10% in value over the next twelve months, from investing via the ETF versus the open-end funds?

D.Provide three reasons why the S&P 500 ETF may be a better investment vehicle than the above three open-end funds, and two reasons why it may be a less desirable investment vehicle than the above three open-end funds.

  1. (20 points) Below are yearly data from 2005 through 2014 (10 years) on three asset classes.

Treasury BillsS&P 1500Frontier Equity Markets

Geometric Mean Return 3.00%8.40%12.50%

Arithmetic Mean Return 3.00%8.75%12.90%

Standard Deviation NA16.00%32.20%

Semi-Standard Deviation NA11.50%30.00%

Return/Risk 'Sharpe' Ratio NA ______

Answer the following questions using the data above:

  1. If you had invested $1,000 in an S&P 1500 index fund and another $1,000 in a Frontier Markets index fund on January 1, 2004 how much would these $1,000 amounts been worth in nominal terms at the end of 2014?
  2. Suppose the cumulative inflation rate from 2004 – 2014 was 25 percent. What would be the real rates of return on the S&P 1500 and Frontier equity markets?
  3. If you were to use the above data to forecast an expected return for the S&P 1500 then what would be your forecasted expected return? Briefly explain.
  4. Interpret the meanings of the standard deviation of 16.00% for the S&P 1500 and the semi-standard deviation for the Frontier Equity Index of 30.00%.
  5. Suppose the returns for the S&P 1500 exhibit a statistically significant negative skewness while those for the Frontier Equity Market index reveal a statistically significant positive skewness. Interpret the standard deviations for these two asset classes in light of their respective skewness.’ Which asset class is riskier?
  1. (25 points) The following table provides data on three risky asset classes: small cap stocks as represented by the Russell 2000 Index; investment grade corporate bonds as represented by the Dow Jones Corporate Bond Index; and developed country equities as represented by the EAFE Stock Market Index.

The top part of the table presents information on expected returns, risks as measured by standard deviations and Sharpe ratios for each of the asset classes. The bottom part of the table presents information on the return correlations between the asset classes.

Russell 2000 DJ Corporate Bond EAFE

Expected Return 10.00% 7.00% 6.00%

Standard Deviation 21.00% 10.00% 35.00%

Sharpe Ratio 0 .48 0 .70 0 .17

Return Correlations

Russell 2000 DJ Bonds EAFE

Russell 2000 1.00 -0.50 +0.80

DJ Bonds -0.50 1.00 0.00

EAFE +0.80 0.00 1.00

  1. Suppose you have a portfolio currently 100 percent invested in investment grade corporate bonds. Which of the other two asset classes provides the greatest potential diversification benefits? Briefly explain.
  2. What does the correlation coefficient of 0.00 between the Dow Jones Corporate Bond Index and EAFE Index mean? What does the correlation coefficient of +0.80 between the Russell 2000 and EAFE indices mean?
  3. If you have a portfolio asset allocation of 40% in investment grade corporate bonds and 60% small capitalization stocks what will be its expected return and risk?
  4. Given the data on expected returns, risks and the Sharpe Ratios from above why would any rational investor hold either US small capitalization stocks, as represented by the Russell 2000 index, or international developed country stocks as represented by the EAFE index?
  1. (25 points) Molly Walker is a successful businesswoman who has accumulated a substantial investment fund totaling $30 million made up of more than 150 individual stocks. She uses three separate investment advisory firms to manage the $30 million fund. Each advisor has $10 million of her money. There is no apparent conformity of strategy, tactics, or style among the three advisors.

Recently she was reviewing the performance of the overall fund, and of each separate advisor. She noted that one advisor, Alec Asset Management (AAM), had consistently outperformed the other two advisors as well as the S&P 500 index. AAM is a ‘bottom-up’ stock picking firm that avoids any attempts at market timing or asset allocation. It focuses exclusively on selecting individual stocks for Molly. It picks about 50 stocks for her, and invests no more than 3% of the $10 million in any one of these 50 stocks.

Molly correctly notes that the reason for AAMs consistent out- performance was because they have been able to identify and select 10-12 stocks each year that registered especially large gains.

Molly has an idea: tell AAM to pick no more than 20 stocks for her. Double the amounts to the stocks AAM really likes and forget the other 30 or so stocks!

  1. Will the restriction to 20 stocks affect the risk of her AAM portfolio? Explain.
  1. A friend of Molly’s liked her idea and said: “Look, why stop at 20 stocks? I think you should tell AAM to pick only 10 stocks for you.” Evaluate her friend’s idea.
  1. Another friend suggested that instead of evaluating each investment advisor independently, it might be better to consider the effects of the change to 20 stocks in the AAM portfolio on her total fund. Evaluate Molly’s idea for AAM in light of her friend’s suggestion.
  1. (20 Points) You are being interviewed for a job with a prestigious investment advisory company. As part of the interview they give you the following information for one of their clients, and ask you to identify whether it is an Investment Objective, Investment Constraint, or Investment Policy. Briefly explain your responses.
  1. Invest 60% in stocks, 35% in bonds, and 5% in alternative investments.
  2. Make sure there is $75,000 in cash on December 31, 2015.
  3. Attempt to earn $500,000 per year on the $5,000,000 investment fund.
  4. If equity markets decline by 15%, then reduce the investment in stocks to 40.
  5. Invest in securities so that the value of the fund will not drop below $5 million.
  6. Maintain the real value, that is, purchasing power of the fund at $5 million.
  1. ( 25 points)Your client, Bo Regard, is building a portfolio that consists of: (1) a portfolio of risky assets comprised of the S&P 500, Barclays U.S. Aggregate Bond, and EAFE index funds and; (2) T-Bills as a risk free asset. The information below refers to these assets.

Risky Asset Portfolios

Risky Asset

Portfolio Number Asset Class Weights Expected Return and Risk

S&P 500/Barclays Bond/EAFE E(Rp)p

150% 30%20% 12.00%20.00%

230% 30% 40% 12.60%25.00% 3 80% 10% 10% 12.00% 7.20%

460% 35% 5% 9.80% 16.60% 5 100% 0% 0% 9.00% 30.00%

The Treasury bill Rate is 3.60%.

  1. Which of the above 5 portfolios of risky assets does not lie on the efficient frontier? Briefly Explain.
  2. Which portfolio is the optimal risky portfolio? Briefly Explain.
  3. Suppose that Bo's degree of risk aversion is 4. What is the optimal allocation for Bo between the risky portfolio and the Treasury bill?
  4. What will be the expected return and risk on Bo's complete portfolio? What will be his asset allocations?
  1. (20 points) Abigail Grace has a $900,000 fully diversified portfolio. She recently inherited ABC common stock worth $100,000. Her investment advisor provided her with the following information :

Return and Risk Characteristics

Expected Monthly ReturnsStandard Deviation of Monthly Returns

Original Portfolio0.67%2.37%

ABC Company Stock1.25%2.95%

Her advisor also estimates the correlation coefficient of returns between her original portfolio and ABC Company stock is .40.

Abigail Grace is deciding whether or not to keep the ABC stock.

  1. Calculate the expected return and standard deviation of her new portfolio assuming she plans to keep the ABC stock.
  2. Calculate the covariance of ABC Company Stock return with her original portfolio returns.

If Abigail Grace decides to sell the ABC Company Stock she will invest the proceeds in risk-free government securities yielding 0.42% monthly. If she does this then:

  1. Calculate the expected return and standard deviation of her new portfolio which includes the government securities.
  2. Calculate the co-variance of the government security returns with the original portfolio returns.

Abigail Grace is also considering selling the $100,000 of ABC Company Stock and using the proceeds to acquire $100,000 of XYZ Company Stock. XYZ Company Stock has the same expected return and standard deviation as ABC Company Stock. A friend of hers comments: “It does not matter whether or not you keep the ABC stock or replace it with the XYZ stock.” Do you agree with her friend’s comment? Explain.